Cartesian Tree Matching and Indexing

Authors Sung Gwan Park, Amihood Amir, Gad M. Landau, Kunsoo Park

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Author Details

Sung Gwan Park
  • Seoul National University, Korea
Amihood Amir
  • Bar-Ilan University, Israel
Gad M. Landau
  • University of Haifa, Israel
  • New York University, USA
Kunsoo Park
  • Seoul National University, Korea


S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Cite AsGet BibTex

Sung Gwan Park, Amihood Amir, Gad M. Landau, and Kunsoo Park. Cartesian Tree Matching and Indexing. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a pattern of length m, and multiple pattern matching for a text of length n and k patterns of total length m. We present an O(n+m) time algorithm for single pattern matching, and an O((n+m) log k) deterministic time or O(n+m) randomized time algorithm for multiple pattern matching. We also define an index data structure called Cartesian suffix tree, and present an O(n) randomized time algorithm to build the Cartesian suffix tree. Our efficient algorithms for Cartesian tree matching use a representation of the Cartesian tree, called the parent-distance representation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Cartesian tree matching
  • Pattern matching
  • Indexing
  • Parent-distance representation


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